Josh.

Josh. is a clerk's shorthand for the given name Joshua. Writers shortened common first names to save time and ink, usually by keeping the first letters and the last one or two, often with the final letters raised above the line.

Name lists also give Josh, without a period, as a contraction of Josiah, and American clerks often put a period after contractions too. So Josh. can stand for Josiah as well; look for the name written in full in other records before deciding.